Abstract Amplitude versus offset (AVO) curves are extracted from 2.5-D finite-difference simulations of ground-penetrating radar (GPR) reflection responses, of a layered model, to horizontal transverse-electric dipole excitation at the air-earth interface. The model parameterization is in terms of Cole-Cole relaxation mechanisms. This allows explicit separation of the effects, of conductivity and the frequency-dependent components of the complex dielectric permittivity and of the complex magnetic permeability, in reflection responses as a function of antenna separation. The amplitude and phase effects of antenna directivity are automatically incorporated into the simulated responses. Reflections associated with contrasts in dielectric and magnetic relaxations are much smaller than those associated with contrasts in permittivity, conductivity, and permeability. For typical earth materials, attenuation of propagating GPR waves is most strongly influenced by conductivity, followed by dielectric relaxation, followed by magnetic relaxation. Reflection magnitudes and AVO curve shapes are very different depending on the contrast in electromagnetic properties that caused the reflection. Thus, the potential is shown for extraction of detailed electromagnetic properties from GPR AVO observations. It is necessary to use frequency-dependent simulations/predictions in analysis of field GPR data when amplitude information is to be interpreted in terms of the distribution of electromagnetic properties.